Additional scaled solutions to Richards’ equation for infiltration and drainage

Warrick and Hussen developed in the nineties of the last century a method to scale Richards’ equation (RE) for similar soils. In this paper, new scaled solutions are added to the method of Warrick and Hussen considering a wider range of soils regardless of their dissimilarity. Gardner–Kozeny hydraulic functions are adopted instead of Brooks–Corey functions used originally by Warrick and Hussen. These functions allow to reduce the dependence of the scaled RE on the soil properties. To evaluate the proposed method (PM), the scaled RE was solved numerically using a finite difference method with a fully implicit scheme. Three cases were considered: constant-head infiltration, constant-flux infiltration, and drainage of an initially uniform wet soil. The results for five texturally different soils ranging from sand to clay (adopted from the literature) showed that the scaled solutions were invariant to a satisfactory degree. However, slight deviations were observed mainly for the sandy soil. Moreover, the scaled solutions deviated when the soil profile was initially wet in the infiltration case or when deeply wet in the drainage condition. Based on the PM, a Philip-type model was also developed to approximate RE solutions for the constant-head infiltration. The model showed a good agreement with the scaled RE for the same range of soils and conditions, however only for Gardner–Kozeny soils. Such a procedure reduces numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils.

► A new method for scaling Richards’ equation (RE) have been developed in this manuscript.
► This method goes beyond previously developed methods to applications for dissimilar soils.
► Using this method, a Philip-type model has been developed for constant-head infiltration.
► The method opens a new window to obtain approximate solutions of the highly nonlinear RE.